X+x+4x2=8

Solution for X+x+4x2=8 equation:

X+X+4X^2=8

We move all terms to the left:

X+X+4X^2-(8)=0

We add all the numbers together, and all the variables

4X^2+2X-8=0

a = 4; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·4·(-8)
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{33}}{2*4}=\frac{-2-2\sqrt{33}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{33}}{2*4}=\frac{-2+2\sqrt{33}}{8}
$